Specifies 2D transformations of a coordinate system. More...

Public Types
enum	TransformationType

Public Methods
	QTransform ()

	QTransform (const QMatrix &matrix)

	QTransform (qreal m11, qreal m12, qreal m13, qreal m21, qreal m22, qreal m23, qreal m31, qreal m32, qreal m33=1.0)

	QTransform (qreal m11, qreal m12, qreal m21, qreal m22, qreal dx, qreal dy)

QTransform	adjoint () const

qreal	det () const

qreal	determinant () const

qreal	dx () const

qreal	dy () const

QTransform	inverted (bool *invertible=nullptr) const

bool	isAffine () const

bool	isIdentity () const

bool	isInvertible () const

bool	isRotating () const

bool	isScaling () const

bool	isTranslating () const

qreal	m11 () const

qreal	m12 () const

qreal	m13 () const

qreal	m21 () const

qreal	m22 () const

qreal	m23 () const

qreal	m31 () const

qreal	m32 () const

qreal	m33 () const

QLine	map (const QLine &line) const

QLineF	map (const QLineF &line) const

QPainterPath	map (const QPainterPath &path) const

QPoint	map (const QPoint &point) const

QPointF	map (const QPointF &point) const

QPolygon	map (const QPolygon &polygon) const

QPolygonF	map (const QPolygonF &polygon) const

QRegion	map (const QRegion &region) const

void	map (int x, int y, int tx, int ty) const

void	map (qreal x, qreal y, qreal tx, qreal ty) const

QRect	mapRect (const QRect &rect) const

QRectF	mapRect (const QRectF &rect) const

QPolygon	mapToPolygon (const QRect &rect) const

	operator QVariant () const

bool	operator!= (const QTransform &transform) const

QTransform	operator* (const QTransform &transform) const

QTransform &	operator*= (const QTransform &transform)

QTransform &	operator*= (qreal factor)

QTransform &	operator+= (qreal delta)

QTransform &	operator-= (qreal delta)

QTransform &	operator/= (qreal factor)

QTransform &	operator= (const QTransform &other)

bool	operator== (const QTransform &transform) const

void	reset ()

QTransform &	rotate (qreal angle, Qt::Axis axis=Qt::ZAxis)

QTransform &	rotateRadians (qreal angle, Qt::Axis axis=Qt::ZAxis)

QTransform &	scale (qreal sx, qreal sy)

void	setMatrix (qreal m11, qreal m12, qreal m13, qreal m21, qreal m22, qreal m23, qreal m31, qreal m32, qreal m33)

QTransform &	shear (qreal sh, qreal sv)

const QMatrix &	toAffine () const

QTransform &	translate (qreal dx, qreal dy)

QTransform	transposed () const

TransformationType	type () const

Static Public Methods
static QTransform	fromScale (qreal sx, qreal sy)

static QTransform	fromTranslate (qreal dx, qreal dy)

static bool	quadToQuad (const QPolygonF &quad1, const QPolygonF &quad2, QTransform &result)

static bool	quadToSquare (const QPolygonF &quad, QTransform &result)

static bool	squareToQuad (const QPolygonF &quad, QTransform &result)

Related Functions
These are not member functions
QLine	operator* (const QLine &line, const QTransform &matrix)

QLineF	operator* (const QLineF &line, const QTransform &matrix)

QPainterPath	operator* (const QPainterPath &path, const QTransform &matrix)

QPoint	operator* (const QPoint &point, const QTransform &matrix)

QPointF	operator* (const QPointF &point, const QTransform &matrix)

QPolygon	operator* (const QPolygon &polygon, const QTransform &matrix)

QPolygonF	operator* (const QPolygonF &polygon, const QTransform &matrix)

QRegion	operator* (const QRegion &region, const QTransform &matrix)

QDataStream &	operator<< (QDataStream &stream, const QTransform &matrix)

QDataStream &	operator>> (QDataStream &stream, QTransform &matrix)

bool	qFuzzyCompare (const QTransform &transform1, const QTransform &transform2)

uint	qHash (const QTransform &key, uint seed=0)

Detailed Description

The QTransform class specifies 2D transformations of a coordinate system. A transformation specifies how to translate, scale, shear, rotate or project the coordinate system, and is typically used when rendering graphics. QTransform is a true 3x3 matrix, allowing perspective transformations.

QTransform's toAffine() method allows converting QTransform to QMatrix. If a perspective transformation has been specified on the matrix, then the conversion will cause loss of data.

A QTransform object can be built using the setMatrix(), scale(), rotate(), translate() and shear() methods. Alternatively, it can be built by applying Basic Matrix Operations. The matrix can also be defined when constructed, and it can be reset to the identity matrix (the default) using the reset() method.

The QTransform class supports mapping of graphic primitives. A given point, line, polygon, region, or painter path can be mapped to the coordinate system defined by this matrix using the map() method. In case of a rectangle, its coordinates can be transformed using the mapRect() method. A rectangle can also be transformed into a polygon (mapped to the coordinate system defined by this matrix), using the mapToPolygon() method.

QTransform provides the isIdentity() method which returns true if the matrix is the identity matrix, and the isInvertible() method which returns true if the matrix is non-singular (i.e. AB = BA = I). The inverted() method returns an inverted copy of this matrix if it is invertible (otherwise it returns the identity matrix), and adjoint() returns the matrix's classical adjoint. In addition, QTransform provides the determinant() method which returns the matrix's determinant.

The QTransform class supports matrix multiplication, addition and subtraction, and objects of the class can be streamed as well as compared.

Rendering Graphics Using QPainter

When rendering graphics the matrix defines the transformations but the actual transformation is performed by the drawing routines in QPainter.

By default, QPainter operates on the associated device's own coordinate system. The standard coordinate system of a QPaintDevice has its origin located at the top-left position. The x value increases to the right and the y value increases downward. For a complete description refer to the coordinate system documentation.

QPainter has methods to translate, scale, shear, and rotate the coordinate system without using a QTransform.

void SimpleTransformation::paintEvent(QPaintEvent *)
{
   QPainter painter(this);
   painter.setPen(QPen(Qt::blue, 1, Qt::DashLine));
   painter.drawRect(0, 0, 100, 100);
 
   painter.rotate(45);
 
   painter.setFont(QFont("Helvetica", 24));
   painter.setPen(QPen(Qt::black, 1));
   painter.drawText(20, 10, "QTransform");
}

Use QTransform with QPainter

Although the methods in QPainter are available, it can be more efficient to build a QTransform and call QPainter::setTransform() to perform multiple transform operations.

void CombinedTransformation::paintEvent(QPaintEvent *)
{
   QPainter painter(this);
   painter.setPen(QPen(Qt::blue, 1, Qt::DashLine));
   painter.drawRect(0, 0, 100, 100);
 
   QTransform transform;
   transform.translate(50, 50);
   transform.rotate(45);
   transform.scale(0.5, 1.0);
   painter.setTransform(transform);
 
   painter.setFont(QFont("Helvetica", 24));
   painter.setPen(QPen(Qt::black, 1));
   painter.drawText(20, 10, "QTransform");
}

Basic Matrix Operations

A QTransform object contains a 3 x 3 matrix. The m31 (dx) and m32 (dy) elements specify horizontal and vertical translation. The m11 and m22 elements specify horizontal and vertical scaling. The m21 and m12 elements specify horizontal and vertical shearing. And finally, the m13 and m23 elements specify horizontal and vertical projection, with m33 as an additional projection factor.

QTransform transforms a point in the plane to another point using the following formulas:

x' = m11*x + m21*y + dx
y' = m22*y + m12*x + dy
 
if (is not affine) {
    w' = m13*x + m23*y + m33
    x' /= w'
    y' /= w'
}

The point (x, y) is the original point, and (x', y') is the transformed point. (x', y') can be transformed back to (x, y) by performing the same operation on the inverted() matrix.

The various matrix elements can be set when constructing the matrix, or by using the setMatrix() method later on. They can also be manipulated using the translate(), rotate(), scale() and shear() methods. The currently set values can be retrieved using the m11(), m12(), m13(), m21(), m22(), m23(), m31(), m32(), m33(), dx() and dy() methods.

Translation is the simplest transformation. Setting dx and dy will move the coordinate system dx units along the X axis and dy units along the Y axis. Scaling can be done by setting m11 and m22. For example, setting m11 to 2 and m22 to 1.5 will double the height and increase the width by 50%. The identity matrix has m11, m22, and m33 set to 1 (all others are set to 0) mapping a point to itself. Shearing is controlled by m12 and m21. Setting these elements to values different from zero will twist the coordinate system. Rotation is achieved by setting both the shearing factors and the scaling factors. Perspective transformation is achieved by setting both the projection factors and the scaling factors.

The following table is the combined transformations example using basic matrix operations.

void BasicOperations::paintEvent(QPaintEvent *)
{
   double pi = 3.14;
 
   double a    = pi/180 * 45.0;
   double sina = sin(a);
   double cosa = cos(a);
 
   QTransform translationTransform(1, 0, 0, 1, 50.0, 50.0);
   QTransform rotationTransform(cosa, sina, -sina, cosa, 0, 0);
   QTransform scalingTransform(0.5, 0, 0, 1.0, 0, 0);
 
   QTransform transform;
   transform = scalingTransform * rotationTransform * translationTransform;
 
   QPainter painter(this);
   painter.setPen(QPen(Qt::blue, 1, Qt::DashLine));
   painter.drawRect(0, 0, 100, 100);
 
   painter.setTransform(transform);
 
   painter.setFont(QFont("Helvetica", 24));
   painter.setPen(QPen(Qt::black, 1));
   painter.drawText(20, 10, "QTransform");
}

See also: QPainter, Coordinate System

Member Enumeration Documentation

enum QTransform::TransformationType

Constant	Value
`QTransform::TxNone`	`0x00`
`QTransform::TxTranslate`	`0x01`
`QTransform::TxScale`	`0x02`
`QTransform::TxRotate`	`0x04`
`QTransform::TxShear`	`0x08`
`QTransform::TxProject`	`0x10`

Constructor & Destructor Documentation

QTransform::QTransform ( )

Constructs an identity matrix. All elements are set to zero except m_11, m_22, and m_33 which are set to 1.

See also: reset()

QTransform::QTransform	(	qreal	m11,
		qreal	m12,
		qreal	m13,
		qreal	m21,
		qreal	m22,
		qreal	m23,
		qreal	m31,
		qreal	m32,
		qreal	m33 = `1.0`
	)

Constructs a matrix with the elements, m11, m12, m13, m21, m22, m23, m31, m32, m33.

See also: setMatrix()

QTransform::QTransform	(	qreal	m11,
		qreal	m12,
		qreal	m21,
		qreal	m22,
		qreal	dx,
		qreal	dy
	)

Constructs a matrix with the elements, m11, m12, m21, m22, dx and dy.

See also: setMatrix()

QTransform::QTransform ( const QMatrix & matrix )

explicit

Constructs a matrix that is a copy of the given matrix. The values for m13, m23, and m33 are set to 0, 0, and 1 respectively.

Method Documentation

QTransform QTransform::adjoint ( ) const

nodiscard

Returns the adjoint of this matrix.

qreal QTransform::det ( ) const

inlinedeprecated

Deprecated:: Returns the matrix's determinant. Use determinant() instead.

qreal QTransform::determinant ( ) const

inline

Returns the matrix's determinant.

qreal QTransform::dx ( ) const

inline

Returns the horizontal translation factor.

See also: m31(), translate()

qreal QTransform::dy ( ) const

inline

Returns the vertical translation factor.

See also: translate()

QTransform QTransform::fromScale	(	qreal	sx,
		qreal	sy
	)

static

Creates a matrix which corresponds to a scaling of sx horizontally and sy vertically. This is equivalent to calling QTransform().scale(sx, sy) but slightly faster.

QTransform QTransform::fromTranslate	(	qreal	dx,
		qreal	dy
	)

static

Creates a matrix which corresponds to a translation of dx along the x axis and dy along the y axis. This is equivalent to calling QTransform().translate(dx, dy) but slightly faster.

QTransform QTransform::inverted ( bool * invertible = nullptr ) const

nodiscard

Returns an inverted copy of this matrix.

If the matrix is singular (not invertible), the returned matrix is the identity matrix. If invertible is valid (i.e. not 0), its value is set to true if the matrix is invertible, otherwise it is set to false.

See also: isInvertible()

bool QTransform::isAffine ( ) const

inline

Returns true if the matrix represent an affine transformation, otherwise returns false.

bool QTransform::isIdentity ( ) const

inline

Returns true if the matrix is the identity matrix, otherwise returns false.

See also: reset()

bool QTransform::isInvertible ( ) const

inline

Returns true if the matrix is invertible, otherwise returns false.

See also: inverted()

bool QTransform::isRotating ( ) const

inline

Returns true if the matrix represents some kind of a rotating transformation, otherwise returns false.

See also: reset()

bool QTransform::isScaling ( ) const

inline

Returns true if the matrix represents a scaling transformation, otherwise returns false.

See also: reset()

bool QTransform::isTranslating ( ) const

inline

Returns true if the matrix represents a translating transformation, otherwise returns false.

See also: reset()

qreal QTransform::m11 ( ) const

inline

Returns the horizontal scaling factor.

See also: scale()

qreal QTransform::m12 ( ) const

inline

Returns the vertical shearing factor.

See also: shear()

qreal QTransform::m13 ( ) const

inline

Returns the horizontal projection factor.

See also: translate()

qreal QTransform::m21 ( ) const

inline

Returns the horizontal shearing factor.

See also: shear()

qreal QTransform::m22 ( ) const

inline

Returns the vertical scaling factor.

See also: scale()

qreal QTransform::m23 ( ) const

inline

Returns the vertical projection factor.

See also: translate()

qreal QTransform::m31 ( ) const

inline

Returns the horizontal translation factor.

See also: dx(), translate()

qreal QTransform::m32 ( ) const

inline

Returns the vertical translation factor.

See also: dy(), translate()

qreal QTransform::m33 ( ) const

inline

Returns the division factor.

See also: translate()

QLine QTransform::map ( const QLine & line ) const

Creates and returns a QLineF object that is a copy of the given line mapped into the coordinate system defined by this matrix.

QLineF QTransform::map ( const QLineF & line ) const

Creates and returns a QLine object that is a copy of the given line, mapped into the coordinate system defined by this matrix. The transformed coordinates are rounded to the nearest integer.

QPainterPath QTransform::map ( const QPainterPath & path ) const

Creates and returns a QPainterPath object that is a copy of the given path, mapped into the coordinate system defined by this matrix.

QPoint QTransform::map ( const QPoint & point ) const

Creates and returns a QPoint object that is a copy of the given point, mapped into the coordinate system defined by this matrix. The transformed coordinates are rounded to the nearest integer.

QPointF QTransform::map ( const QPointF & point ) const

Creates and returns a QPointF object that is a copy of the given point mapped into the coordinate system defined by this matrix.

QPolygon QTransform::map ( const QPolygon & polygon ) const

Creates and returns a QPolygon object that is a copy of the given polygon, mapped into the coordinate system defined by this matrix. The transformed coordinates are rounded to the nearest integer.

QPolygonF QTransform::map ( const QPolygonF & polygon ) const

Creates and returns a QPolygonF object that is a copy of the given polygon, mapped into the coordinate system defined by this matrix.

QRegion QTransform::map ( const QRegion & region ) const

Creates and returns a QRegion object that is a copy of the given region, mapped into the coordinate system defined by this matrix. Calling this method can be rather expensive if rotations or shearing are used.

void QTransform::map	(	int	x,
		int	y,
		int *	tx,
		int *	ty
	)		const

Maps the given coordinates x and y into the coordinate system defined by this matrix. The resulting values are put in tx and ty, respectively. The transformed coordinates are rounded to the nearest integer.

void QTransform::map	(	qreal	x,
		qreal	y,
		qreal *	tx,
		qreal *	ty
	)		const

Maps the given coordinates x and y into the coordinate system defined by this matrix. The resulting values are put into tx and ty respectively.

The coordinates are transformed using the following formulas. The point (x, y) is the original point, and (x', y') is the transformed point.

x' = m11*x + m21*y + dx
y' = m22*y + m12*x + dy
 
if (is not affine) {
    w' = m13*x + m23*y + m33
    x' /= w'
    y' /= w'
}

See also: Basic Matrix Operations

QRect QTransform::mapRect ( const QRect & rect ) const

Creates and returns a QRect object that is a copy of the given rect, mapped into the coordinate system defined by this matrix. The transformed coordinates are rounded to the nearest integer.

QRectF QTransform::mapRect ( const QRectF & rect ) const

Creates and returns a QRectF object that is a copy of the given rect, mapped into the coordinate system defined by this matrix. If rotation or shearing has been specified the bounding rectangle is returned. To retrieve the exact region the given rectangle maps to, call mapToPolygon() instead.

The rectangle's coordinates are transformed using the following formulas.

x' = m11*x + m21*y + dx
y' = m22*y + m12*x + dy
 
if (is not affine) {
    w' = m13*x + m23*y + m33
    x' /= w'
    y' /= w'
}

See also: mapToPolygon()

QPolygon QTransform::mapToPolygon ( const QRect & rect ) const

Creates and returns a QPolygon representation of the given rect, mapped into the coordinate system defined by this matrix. Polygons and rectangles behave slightly differently when transformed (due to integer rounding). This means calling matrix.map(QPolygon(rect)) is not always the same as calling matrix.mapToPolygon(rect).

The rectangle's coordinates are transformed using the following formulas.

x' = m11*x + m21*y + dx
y' = m22*y + m12*x + dy
 
if (is not affine) {
    w' = m13*x + m23*y + m33
    x' /= w'
    y' /= w'
}

See also: mapRect()

QTransform::operator QVariant ( ) const

Returns the transform as a QVariant.

bool QTransform::operator!= ( const QTransform & transform ) const

Returns true if this matrix is not equal to the given transform, otherwise returns false.

QTransform QTransform::operator* ( const QTransform & transform ) const

Returns the result of multiplying this matrix by the given transform. Matrix multiplication is not commutative, for example a*b != b*a.

QTransform & QTransform::operator*= ( const QTransform & transform )

Returns the result of multiplying this matrix by the given transform.

QTransform & QTransform::operator*= ( qreal factor )

inline

Returns the result of performing an element-wise multiplication of this matrix with the given factor.

QTransform & QTransform::operator+= ( qreal delta )

inline

Returns the matrix obtained by adding the given delta to each element of this matrix.

QTransform & QTransform::operator-= ( qreal delta )

inline

Returns the matrix obtained by subtracting the given delta from each element of this matrix.

QTransform & QTransform::operator/= ( qreal factor )

inline

Returns the result of performing an element wise division of this matrix by the given factor.

QTransform & QTransform::operator= ( const QTransform & other )

Copy assigns from other and returns a reference to this object.

bool QTransform::operator== ( const QTransform & transform ) const

Returns true if this matrix is equal to the given matrix, otherwise returns false.

bool QTransform::quadToQuad	(	const QPolygonF &	quad1,
		const QPolygonF &	quad2,
		QTransform &	result
	)

static

Computes a transformation matrix which transforms the given quad1 to quad2. If this can be created the output will be placed in result and return value will be true. If no transformation can be created for the given quad the return value is false.

See also: squareToQuad(), quadToSquare()

bool QTransform::quadToSquare	(	const QPolygonF &	quad,
		QTransform &	result
	)

static

Computes a transformation matrix which transforms the given quad to a one unit square. If this can be created the output will be placed in result and return value will be true. If no transformation can be created for the given quad the return value is false.

See also: squareToQuad(), quadToQuad()

void QTransform::reset ( )

Resets the matrix to an identity matrix, i.e. all elements are set to zero, except m11 and m22 (specifying the scale) and m33 which are set to 1.

See also: QTransform(), isIdentity()

QTransform & QTransform::rotate	(	qreal	angle,
		Qt::Axis	axis = `Qt::ZAxis`
	)

Rotates the coordinate system counterclockwise by the given angle about the specified axis and returns a reference to the matrix. If you apply a QTransform to a point defined in widget coordinates, the direction of the rotation will be clockwise because the y-axis points downwards. The angle is specified in degrees.

See also: setMatrix()

QTransform & QTransform::rotateRadians	(	qreal	angle,
		Qt::Axis	axis = `Qt::ZAxis`
	)

Rotates the coordinate system counterclockwise by the given angle about the specified axis and returns a reference to the matrix. If you apply a QTransform to a point defined in widget coordinates, the direction of the rotation will be clockwise because the y-axis points downwards.

The angle is specified in radians.

See also: setMatrix()

QTransform & QTransform::scale	(	qreal	sx,
		qreal	sy
	)

Scales the coordinate system by sx horizontally and sy vertically, and returns a reference to the matrix.

See also: setMatrix()

void QTransform::setMatrix	(	qreal	m11,
		qreal	m12,
		qreal	m13,
		qreal	m21,
		qreal	m22,
		qreal	m23,
		qreal	m31,
		qreal	m32,
		qreal	m33
	)

Sets the matrix elements to the specified values, m11, m12, m13 m21, m22, m23, m31, m32, and m33. This method replaces the previous values in the matrix.

See also: QTransform()

QTransform & QTransform::shear	(	qreal	sh,
		qreal	sv
	)

Shears the coordinate system by sh horizontally and sv vertically, and returns a reference to the matrix.

See also: setMatrix()

bool QTransform::squareToQuad	(	const QPolygonF &	quad,
		QTransform &	result
	)

static

Computes a transformation matrix which transforms a one unit square to the given quad. If this can be created the output will be placed in result and return value will be true. If no transformation can be created for the given quad the return value is false.

See also: quadToSquare(), quadToQuad()

const QMatrix & QTransform::toAffine ( ) const

Returns the current QTransform as an affine matrix.

Warning: If a perspective transformation has been specified, then the conversion will cause loss of data.

QTransform & QTransform::translate	(	qreal	dx,
		qreal	dy
	)

Moves the coordinate system dx along the x axis and dy along the y axis, and returns a reference to the matrix.

See also: setMatrix()

QTransform QTransform::transposed ( ) const

nodiscard

Returns the transpose of this matrix.

TransformationType QTransform::type ( ) const

Returns the transformation type of this matrix.

The transformation type is the highest enumeration value capturing all of the matrix's transformations. For example, if the matrix both scales and shears, the type would be TxShear, because TxShear has a higher enumeration value than TxScale.

Knowing the transformation type of a matrix is useful for optimization: you can often handle specific types more optimally than handling the generic case.

Friends And Related Function Documentation

QLine operator*	(	const QLine &	line,
		const QTransform &	matrix
	)

See also: QTransform::map()

QLineF operator*	(	const QLineF &	line,
		const QTransform &	matrix
	)

See also: QTransform::map()

QPainterPath operator*	(	const QPainterPath &	path,
		const QTransform &	matrix
	)

See also: QTransform::map()

QPoint operator*	(	const QPoint &	point,
		const QTransform &	matrix
	)

See also: QTransform::map()

QPointF operator*	(	const QPointF &	point,
		const QTransform &	matrix
	)

See also: QTransform::map()

QPolygon operator*	(	const QPolygon &	polygon,
		const QTransform &	matrix
	)

See also: QTransform::map()

QPolygonF operator*	(	const QPolygonF &	polygon,
		const QTransform &	matrix
	)

See also: QTransform::map()

QRegion operator*	(	const QRegion &	region,
		const QTransform &	matrix
	)

See also: QTransform::map()

QDataStream & operator<<	(	QDataStream &	stream,
		const QTransform &	matrix
	)

Refer to Serializing Data Types for additional information.

QDataStream & operator>>	(	QDataStream &	stream,
		QTransform &	matrix
	)

Refer to Serializing Data Types for additional information.

bool qFuzzyCompare	(	const QTransform &	transform1,
		const QTransform &	transform2
	)

uint qHash	(	const QTransform &	key,
		uint	seed = `0`
	)

Public Types

Public Methods

Static Public Methods

Related Functions

Detailed Description

Rendering Graphics Using QPainter

Use QTransform with QPainter

Basic Matrix Operations

Member Enumeration Documentation

Constructor & Destructor Documentation

Method Documentation

Friends And Related Function Documentation